Electrical-control of third-order nonlinearity via Fano interference

TL;DR

The paper addresses the need for electrically tunable third-order nonlinearity in continuous-variable photonic quantum computing. It demonstrates a plasmonic MNP dimer coupled to a narrow-linewidth QO, where Fano interference controlled by Stark-shifted level spacing $Ω_{QO}$ enables suppression (at $Ω_{QO}=3ω$) or enhancement (near $Ω_{QO}≈2.99ω$) of THG at the nonlinear frequency $3ω$, with picosecond response. The work combines an analytical model with exact 3D Maxwell/FDTD simulations, and shows that ensemble positioning of QOs introduces phase differences that can degrade the enhancement. The results point to a fast, compact nonlinear gate for MBQC, where auxiliary nonlinear pulses can be generated off-circuit and coupled into fragile quantum states with minimal perturbation to the linear response.

Abstract

Programmable photonic computers necessitate the integration of electrically-tunable compact components into the photonic devices. In the state-of-the-art photonic quantum computers~(PQCs), phase-shift and displacement gates can be implemented in an electrically-programmable way. An efficient PQC, however, necessitates also the tuning of third or higher order nonlinearity for implementing continuous-variable~(CV) gates at a shorter sequence. Here, we demonstrate that such an optical component can be designed using Fano interference and Stark effect in a nonlinear nano-plasmonic system. We study the coupling of a broadband bright plasmon mode to a narrow linewidth quantum object(s), QO(s). We show that by shifting the level-spacing of the QO via Stark effect, one can continuously tune the third-order nonlinearity gate within a picosecond response time. We also present finite-difference time domain~(FDTD) simulations that take the retardation effects into account. In addition, we also show that enhancement due to Fano interference degrades if the QOs are positioned randomly as each QO introduces different phases. This reveals the importance of the spatial extent of the QO-ensemble to be employed in the experiments.

Figures (4)

• Figure 1: (a) Control of third harmonic generation signal by a quantum object (QO) residing at the hotspot of a metal nanoparticle (MNP) dimer. Pump photons of frequency $\omega$ are localized at the hotspot as plasmon oscillations takes place in the $\Omega_1$-mode. Localization gives rise to several orders of magnitude enhancement in the third harmonic generation (THG). The level-spacing of the QO is chosen around the THG frequency, $\Omega_{\rm QO}\sim 3\omega$. Level-spacing controls the nonlinear signal. $\Omega_{\rm QO}= 3\omega$ turns off the THG while $\Omega_{\rm QO}\simeq 2.99\omega$ enhances the THG. Applied voltage shifts the level-spacing shibata2013largelarocque2024tunablemiller1985electric. (b) The plasmon modes and corresponding fundamental and third harmonic frequencies.
• Figure 2: Demonstration of the two opposite phenomena, (a) suppression and (b) enhancement of the third harmonic signal, by the exact solutions of the 3D nonlinear Maxwell equations. For two different choices of the quantum object level-spacing (a) $\Omega_{\rm QO}=1696$ THz and (b) $\Omega_{\rm QO}=1694$ THz, suppression and enhancement are observed at the same pump frequency $3\omega=1695.8$ THz.
• Figure 3: Continuous electrical tuning of the third harmonic intensity by shifting the level-spacing of the QO. Different level-spacing results in different path interference effects that can be explainv ia the denominator of Eq. (\ref{['eq18']}). Such a tuning can be performed by applying a potential-difference on the QO shibata2013largelarocque2024tunablemiller1985electric that shifts the level-spacing. The required voltage ---calculated crudely from the $\Delta \Omega_{\rm QE}$-$V$ graph presented in the experiments shibata2013largelarocque2024tunablemiller1985electric--- is less than 1 Volt. The presented data is the exact solution of the 3D nonlinear Maxwell equations for the system depicted in Fig. \ref{['fig1']}a.
• Figure 4: (a) Fano enhancement of the THG when more than one QOs are placed in the gap at different positioned. (b) Because of the retardation effect, QOs located at different positions take different phases. There is still a very strong Fano enhancement but it degrades by a factor of 1/2 with respect to a single QO case. Exact solutions of the 3D nonlinear Maxwell equations.